For a new determination of the Avogadro constant to play a role in the future redefinition and realization of the mass unit, the mass measurements involved need to be carried out at a very high level of accuracy. From a mass comparison among two 1 kg 28Si spheres and the 1 kg platinum–iridium (Pt/Ir) mass standards, the mass of the spheres must be determined with a combined standard uncertainty of less than 5 µg. The BIPM, the PTB and the NMIJ have carried out such a state-of-the-art mass comparison in air and under vacuum in order to reach this target set by the International Avogadro Coordination (IAC). The results obtained for the spheres AVO28-S5 and AVO28-S8 involved in the comparison have demonstrated that by using air buoyancy artefacts and sorption artefacts it is possible to achieve a relative uncertainty of 4.1 × 10−9. The reference value for each sphere has been determined, taking into account the traceability of the masses to the International Prototype of the kilogram, , in due consideration of the correlations among 17 standards used directly or indirectly in this comparison.

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The results are presented of the key comparison EURAMET 1031 (EURAMET.M.D-K1.1) that covered the measurements of density and volume of silicon spheres of three different masses at 20 °C and 101325 Pa. The volume and density determinations of 15 national metrology institutes (NMIs) were checked and linked to the CCM.D-K1 key comparison. The measurements were carried out near 20 °C and at atmospheric pressure by the hydrostatic method in the time interval from 16 May 2008 to 18 Jan 2011. The comparison was performed in two petals with three spheres in each petal. The travelling standards of petal 1 have a mass of 1001 g, 200 g and 35 g (Petal 2: 984 g, 239 g, 35 g). Whereas the reference values of the 1 kg travelling standards could be determined by the link to the CCM.D-K1 comparison, the density reference values for the smaller spheres were determined by density comparison to the 1 kg spheres using the pressure-of-flotation method. One result was wrong due to a mistake in the mass determination. Additionally, four of the 57 volume (or density) values were discrepant with En values larger than 1.1, 1.2, 1.3 and 1.6. Five NMIs achieved density uncertainties of about 1 ppm (1 × 10−6 in relative terms) or less for the 1 kg spheres. This satisfies the needs of all customers who wish to calibrate solid density standards for other laboratories. Volume determinations of mass standards, air density artefacts or sorption artefacts should reach an uncertainty of about 1 mm3 in order to reduce the effect on the mass uncertainty to about 1 μg. At least for silicon spheres this is reached by eight NMIs. Due to the higher density of stainless steel this may be different for weights and will be checked within the CCM.D-K3 comparison. The results of the comparison can be used to submit new or improved entries in the calibration measurement capabilities table in the BIPM key comparison database. Main text To reach the main text of this paper, click on Final Report. Note that this text is that which appears in Appendix B of the BIPM key comparison database kcdb.bipm.org/. The final report has been peer-reviewed and approved for publication by the CCM, according to the provisions of the CIPM Mutual Recognition Arrangement (CIPM MRA).